In this paper we obtain the local regularity estimates in Besov spaces of weak solutions for a class of elliptic obstacle problems with variable exponents $p(x)$ . We deal with the case in which the solutions to the obstacle problems satisfy a variational inequality in the following form \(\begin{aligned} \int _{\Omega } \langle A\left (x, Du \right ),~D \left (\varphi -u \right )\rangle {\mathrm{d}}x\geq \int _{\Omega } \langle F,~D \left ( \varphi -u \right )\rangle {\mathrm{d}}x \end{aligned}\) under some proper assumptions on the function $p(x)$ , $A$ , $\varphi $ and $F$ . Moreover, we would like to point out that our results improve the known results for such problems.
